1. 7-5 Indirect Measurement Warm Up Problem of the Day
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up Find the missing value in each proportion. 1. = 2. = 3. = 4. == = = = 6 t __ 18 45 __
t = 15 k 19 __ 20 76 __
k = 5 6 8 __ 42 n __
n = 56 21 11 __ x 44 __
x = 84

3. Problem of the Day
Bryce, Kate, and Annie have drawn rectangles. Each side of Bryce’s rectangle is twice the size of one side of Kate’s. The same side of Kate’s rectangle is congruent to one side of Annie’s. One side of Annie’s rectangle is congruent to one side of Bryce’s. Which two rectangles could be congruent?
Kate’s and Annie’s

4. Learn to use proportions and similar figures to find unknown measures.

5. Vocabulary
indirect measurement

6. One way to find a height that you cannot measure directly is to use similar figures and proportions. This method is called indirect measurement.

7. Additional Example 1: Using Indirect Measurement
Use the similar triangles to find the height of the tree. 6 h __ 2 7 __
Write a proportion using corresponding sides. =
h • 2 = 6 • 7
The cross products are equal.
2h = 42
h is multiplied by 2. 2h 2
___ 42 2
___
Divide both sides by 2 to undo multiplication. =
h = 21
The tree is 21 feet tall.

8. Check It Out: Example 1
Use the similar triangles to find the height of the tree. 6 h __ 3 9 __
Write a proportion using corresponding sides. =
h • 3 = 6 • 9
The cross products are equal.
3h = 54
h is multiplied by 3.
6 ft h 3h 3
___ 54 3
___
Divide both sides by 3 to undo multiplication. =
3 ft ft.
h = 18
The tree is 18 feet tall.

9. Additional Example 2: Measurement Application
A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket?
Write a proportion using corresponding sides. h 4 __
91.5 3
____ =
4 • 91.5 = h • 3
The cross products are equal.
366 = 3h
h is multiplied by 3.
366 3
___ 3h 3
___
Divide both sides by 3 to undo multiplication. =
122 = h
The rocket is 122 feet tall.

10. Write a proportion using corresponding sides. =
Check It Out: Example 2
A building casts a shadow that is 72.5 feet long when a 4-foot model building casts a shadow that is 2 feet long. How tall is the building? h 4 __
72.5 2
____
Write a proportion using corresponding sides. =
4 • 72.5 = h • 2
The cross products are equal.
290 = 2h
h is multiplied by 2. h
72.5 ft ft
4 ft
Divide both sides by 2 to undo multiplication.
290 2
___ 2h 2
___ =
145 = h
The building is 145 feet tall.

11. 1. Use the similar triangles to find the height of the post.
Lesson Quiz
1. Use the similar triangles to find the height of the post.
2. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost? x
15 ft
20 feet
8 ft
6 ft
25 feet